How do you explain Jon Snow's connection to his direwolf, or bran if he isn't Ned's son?

he is still a Stark and remember, his wolf was not with the original litter, Ghost had crawled off on his own.

Also, I forgot where in the text they mention this but Arya is described as looking like Lyanna. Elsewhere in the books Jon is mentioned as looking like Arya. so...Jon looks like Lyanna (perhaps his real mother)